[tex]f(x)=\cos[\ln(x^5)]\implies \stackrel{chain~rule}{\cfrac{df}{dx}=-\sin[\ln(x^5)]\cdot \cfrac{1}{x^5}\cdot 5x^4} \\\\\\ \left. \cfrac{df}{dx}=-\cfrac{5\sin[\ln(x^5)]}{x} \right|_{x=1}\implies -\cfrac{5\sin[\ln(1^5)]}{1}\implies -\cfrac{5\sin(0)}{1}\implies 0[/tex]
